Sub-elliptic boundary value problems in flag domains

Abstract A flag domain in ℝ 3 {\mathbb{R}^{3}} is a subset of the form { stretchy="false">( x , y t stretchy="false">) : < A ⁢ stretchy="false">} {\{(x,y,t):y<A(x)\}} , where → {A\colon\mathbb{R}\to\mathbb{R}} Lipschitz function. We solve Dirichlet and Neumann problems for sub-elliptic Kohn–Laplacian mathsize="160%" stretchy="false">△ ♭ = X 2 + Y {\bigtriangleup^{\flat}=X^{2}+Y^{2}} domains mathvariant="normal">Ω ⊂ {\Omega\subset\mathbb{R}^{3}} with L {L^{2}} -boundary values. also obtain improved regularity solutions to problem if boundary values have first order -Sobolev regularity. Our are obtained as single double layer potentials, which best viewed integral operators on Heisenberg group. develop theory these domains, their boundaries.